The growing prominence of large language models (LLMs) in daily life has heightened concerns that LLMs exhibit many of the same gender-related biases as their creators. In the context of hiring decisions, we quantify the degree to which LLMs perpetuate societal biases and investigate prompt engineering as a bias mitigation technique. Our findings suggest that for a given resumé, an LLM is more likely to hire a female candidate and perceive them as more qualified, but still recommends lower pay relative to male candidates.

Nonlinear Partial Differential Equations (PDEs) are ubiquitous in mathematical physics and engineering. Although Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving PDE problems, they typically struggle to identify multiple distinct solutions, since they are designed to find one solution at a time. To address this limitation, we introduce Deflation-PINNs, a novel framework that integrates a deflation loss with an architecture based on PINNs and Deep Operator Networks (DeepONets). By incorporating a deflation term into the loss function, our method systematically forces the Deflation-PINN to seek and converge upon distinct finitely many solution branches. We provide theoretical evidence on the convergence of our model and demonstrate the efficacy of Deflation-PINNs through numerical experiments on the Landau-de Gennes model of liquid crystals, a system renowned for its complex energy landscape and multiple equilibrium states. Our results show that Deflation-PINNs can successfully identify and characterize multiple distinct crystal structures.

We propose closed-form conditional diffusion models for data assimilation. Diffusion models use data to learn the score function (defined as the gradient of the log-probability density of a data distribution), allowing them to generate new samples from the data distribution by reversing a noise injection process. While it is common to train neural networks to approximate the score function, we leverage the analytical tractability of the score function to assimilate the states of a system with measurements. To enable the efficient evaluation of the score function, we use kernel density estimation to model the joint distribution of the states and their corresponding measurements. The proposed approach also inherits the capability of conditional diffusion models of operating in black-box settings, i.e., the proposed data assimilation approach can accommodate systems and measurement processes without their explicit knowledge. The ability to accommodate black-box systems combined with the superior capabilities of diffusion models in approximating complex, non-Gaussian probability distributions means that the proposed approach offers advantages over many widely used filtering methods. We evaluate the proposed method on nonlinear data assimilation problems based on the Lorenz-63 and Lorenz-96 systems of moderate dimensionality and nonlinear measurement models. Results show the proposed approach outperforms the widely used ensemble Kalman and particle filters when small to moderate ensemble sizes are used.

Large language model-based AI agents are now able to autonomously execute substantial portions of a high energy physics (HEP) analysis pipeline with minimal expert-curated input. Given access to a HEP dataset, an execution framework, and a corpus of prior experimental literature, we find that Claude Code succeeds in automating all stages of a typical analysis: event selection, background estimation, uncertainty quantification, statistical inference, and paper drafting. We argue that the experimental HEP community is underestimating the current capabilities of these systems, and that most proposed agentic workflows are too narrowly scoped or scaffolded to specific analysis structures. We present a proof-of-concept framework, Just Furnish Context (JFC), that integrates autonomous analysis agents with literature-based knowledge retrieval and multi-agent review, and show that this is sufficient to plan, execute, and document a credible high energy physics analysis. We demonstrate this by conducting analyses on open data from ALEPH, DELPHI, and CMS to perform electroweak, QCD, and Higgs boson measurements. Rather than replacing physicists, these tools promise to offload the repetitive technical burden of analysis code development, freeing researchers to focus on physics insight, truly novel method development, and rigorous validation. Given these developments, we advocate for new strategies for how the community trains students, organizes analysis efforts, and allocates human expertise.

We present an AI agentic measurement of the thrust distribution in $e^{+}e^{-}$ collisions at $\sqrt{s}=91.2$~GeV using archived ALEPH data. The analysis and all note writing is carried out entirely by AI agents (OpenAI Codex and Anthropic Claude) under expert physicist direction. A fully corrected spectrum is obtained via Iterative Bayesian Unfolding and Monte Carlo based corrections. This work represents a step toward a theory-experiment loop in which AI agents assist with experimental measurements and theoretical calculations, and synthesize insights by comparing the results, thereby accelerating the cycle that drives discovery in fundamental physics. Our work suggests that precision physics, leveraging the open LEP data and advanced theoretical landscape, provides an ideal testing ground for developing advanced AI systems for scientific applications.

We evaluate GPTutor, an LLM-powered tutoring system for an undergraduate discrete mathematics course. It integrates two LLM-supported tools: a structured proof-review tool that provides embedded feedback on students' written proof attempts, and a chatbot for math questions. In a staggered-access study with 148 students, earlier access was associated with higher homework performance during the interval when only the experimental group could use the system, while we did not observe this performance increase transfer to exam scores. Usage logs show that students with lower self-efficacy and prior exam performance used both components more frequently. Session-level behavioral labels, produced by human coding and scaled using an automated classifier, characterize how students engaged with the chatbot (e.g., answer-seeking or help-seeking). In models controlling for prior performance and self-efficacy, higher chatbot usage and answer-seeking behavior were negatively associated with subsequent midterm performance, whereas proof-review usage showed no detectable independent association. Together, the findings suggest that chatbot-based support alone may not reliably support transfer to independent assessment of math proof-learning outcomes, whereas work-anchored, structured feedback appears less associated with reduced learning.

Accurate calculations of solvation free energies remain a central challenge in molecular simulations, often requiring extensive sampling and numerous alchemical intermediates to ensure sufficient overlap between phase-space distributions of a solute in the gas phase and in solution. Here, we introduce a computational framework based on normalizing flows that directly maps solvent configurations between solutes of different sizes, and compare the accuracy and efficiency to conventional free energy estimates. For a Lennard-Jones solvent, we demonstrate that this approach yields acceptable accuracy in estimating free energy differences for challenging transformations, such as solute growth or increased solute-solute separation, which typically demand multiple intermediate simulation steps along the transformation. Analysis of radial distribution functions indicates that the flow generates physically meaningful solvent rearrangements, substantially enhancing configurational overlap between states in configuration space. These results suggest flow-based models as a promising alternative to traditional free energy estimation methods.

We introduce the first principled framework, Lumos, for specifying and formally certifying Language Model System (LMS) behaviors. Lumos is an imperative probabilistic programming DSL over graphs, with constructs to generate independent and identically distributed prompts for LMS. It offers a structured view of prompt distributions via graphs, forming random prompts from sampled subgraphs. Lumos supports certifying LMS for arbitrary prompt distributions via integration with statistical certifiers. We provide hybrid (operational and denotational) semantics for Lumos, providing a rigorous way to interpret the specifications. Using only a small set of composable constructs, Lumos can encode existing LMS specifications, including complex relational and temporal specifications. It also facilitates specifying new properties - we present the first safety specifications for vision-language models (VLMs) in autonomous driving scenarios developed with Lumos. Using these, we show that the state-of-the-art VLM Qwen-VL exhibits critical safety failures, producing incorrect and unsafe responses with at least 90% probability in right-turn scenarios under rainy driving conditions, revealing substantial safety risks. Lumos's modular structure allows easy modification of the specifications, enabling LMS certification to stay abreast with the rapidly evolving threat landscape. We further integrate a prompt-level deterministic verifier to obtain guarantees over the privacy of the LLM generation distribution over a prompt distribution. Lumos is simple to program in, requiring only a few constructs, as evidenced by state-of-the-art large language models generating correct Lumos specifications in zero-shot settings. Lumos is the first systematic and extensible language-based framework for specifying and certifying LMS behaviors, paving the way for a wider adoption of LMS certification.

Synthetic data can improve generalization when real data is scarce, but excessive reliance may introduce distributional mismatches that degrade performance. In this paper, we present a learning-theoretic framework to quantify the trade-off between synthetic and real data. Our approach leverages algorithmic stability to derive generalization error bounds, characterizing the optimal synthetic-to-real data ratio that minimizes expected test error as a function of the Wasserstein distance between the real and synthetic distributions. We motivate our framework in the setting of kernel ridge regression with mixed data, offering a detailed analysis that may be of independent interest. Our theory predicts the existence of an optimal ratio, leading to a U-shaped behavior of test error with respect to the proportion of synthetic data. Empirically, we validate this prediction on CIFAR-10 and a clinical brain MRI dataset. Our theory extends to the important scenario of domain adaptation, showing that carefully blending synthetic target data with limited source data can mitigate domain shift and enhance generalization. We conclude with practical guidance for applying our results to both in-domain and out-of-domain scenarios.

Magnetic resonance imaging (MRI) has greatly advanced neuroscience research and clinical diagnostics. However, imaging data collected across different scanners, acquisition protocols, or imaging sites often exhibit substantial heterogeneity, known as batch effects or site effects. These non-biological sources of variability can obscure true biological signals, reduce reproducibility and statistical power, and severely impair the generalizability of learning-based models across datasets. Image harmonization is grounded in the central hypothesis that site-related biases can be eliminated or mitigated while preserving meaningful biological information, thereby improving data comparability and consistency. This review provides a comprehensive overview of key concepts, methodological advances, publicly available datasets, and evaluation metrics in the field of MRI harmonization. We systematically cover the full imaging pipeline and categorize harmonization approaches into prospective acquisition and reconstruction, retrospective image-level and feature-level methods, and traveling-subject-based techniques. By synthesizing existing methods and evidence, we revisit the central hypothesis of image harmonization and show that, although site invariance can be achieved with current techniques, further evaluation is required to verify the preservation of biological information. To this end, we summarize the remaining challenges and highlight key directions for future research, including the need for standardized validation benchmarks, improved evaluation strategies, and tighter integration of harmonization methods across the imaging pipeline.

Guidance is a cornerstone of modern diffusion models, playing a pivotal role in conditional generation and enhancing the quality of unconditional samples. However, current approaches to guidance scheduling--determining the appropriate guidance weight--are largely heuristic and lack a solid theoretical foundation. This work addresses these limitations on two fronts. First, we provide a theoretical formalization that precisely characterizes the relationship between guidance strength and classifier confidence. Second, building on this insight, we introduce a stochastic optimal control framework that casts guidance scheduling as an adaptive optimization problem. In this formulation, guidance strength is not fixed but dynamically selected based on time, the current sample, and the conditioning class, either independently or in combination. By solving the resulting control problem, we establish a principled foundation for more effective guidance in diffusion models.

Many existing mechanisms for achieving differential privacy (DP) on infinite-dimensional functional summaries typically involve embedding these functional summaries into finite-dimensional subspaces and applying traditional multivariate DP techniques. These mechanisms generally treat each dimension uniformly and struggle with complex, structured summaries. This work introduces a novel mechanism to achieve pure DP for functional summaries in a separable infinite-dimensional Hilbert space, named the Independent Component Laplace Process (ICLP) mechanism. This mechanism treats the summaries of interest as truly infinite-dimensional functional objects, thereby addressing several limitations of the existing mechanisms. Several statistical estimation problems are considered, and we demonstrate how one can enhance the utility of private summaries by oversmoothing the non-private counterparts. Numerical experiments on synthetic and real datasets demonstrate the effectiveness of the proposed mechanism.

For a 2d gauged sigma model with target space $M$ and discrete gauge group $G$, we consider a generalisation of Vafa's discrete torsion $H^2(BG; U(1))$ that assigns different local discrete torsion phases to different singular loci of the orbifold $M/G$. Our generalised discrete torsion lives in $H^2_G(M; U(1))$, and gives a consistent implementation of Gaberdiel and Kaste's prescription for inserting such local discrete torsion phases by hand at higher genus. We revisit the original application to $T^6/\mathbb{Z}_2^2$ and $T^7/\mathbb{Z}_2^3$ orbifold CFTs, and determine what smooth Calabi-Yau and $G_2$ geometries result from different choices of the generalised discrete torsion. We find that the local discrete torsion phases can be different from each other, but are not completely independent either; in the $T^7/\mathbb{Z}_2^3$ case for example, the orbifold CFTs only realise 3 out of the 9 possible Betti numbers of $G_2$ resolutions constructed by Joyce.

Based on the discovery of high-temperature superconductivity in the bilayer nickelate La$_3$Ni$_2$O$_7$, several Co-based La$_3$Ni$_2$O$_7$-like materials were theoretically predicted as possible high-temperature superconductors by electron doping. Motivated by these findings and the subsequent discovery of superconductivity in the trilayer nickelate La$_4$Ni$_3$O$_{10}$ under high pressure, we propose and investigate a Co-based La$_4$Ni$_3$O$_{10}$-like material. With electron doping to the high-pressure trilayer cobaltate La$_4$Co$_3$O$_{10}$, using density functional theory combined with dynamical mean-field theory (DFT+DMFT), we find that the resulting compound La$_4$Co$_2$NiO$_8$Cl$_2$ exhibits a crystal structure and a strongly correlated electronic structure similar to those of La$_4$Ni$_3$O$_{10}$ under high pressure. This suggests that this new compound may host high-temperature superconductivity.

The detection of high-energy neutrino signals from the nearby Seyfert galaxy NGC 1068 provides us with a unique opportunity to explore nonthermal processes near the center of supermassive black holes. Using the IceCube and Fermi-LAT data, we present general multimessenger constraints on the energetics of cosmic rays and the compactness of the neutrino emission region (${\mathcal R}$), considering not only $pγ$ but also $pp$ processes. Compared to the photohadronic scenario, the hadronuclear scenario can alleviate constraints on the emission region, yielding ${\mathcal R}\lesssim30-70$ for low-$β$ plasma and ${\mathcal R}\lesssim5-50$ for high-$β$ plasma. While our results support the previous conclusion that the photohadronic scenario favors a compact corona with ${\mathcal R}\sim3-10$, these suggest the relevance of further investigations into $pp$ neutrino contributions. When the cosmic-ray spectrum is extended from 1 GeV, we find that the requred cosmic-ray luminosity exceeds the X-ray luminosity for a spectral index of $s_{\rm CR}\gtrsim2$, which challenges some shock acceleration models. We also show that the beta decay scenario is unlikely even if the magnetic field is as strong as the maximum allowed by the Eddington luminosity. Given that NGC 1068 can be established as a neutrino source, our results will provide evidence for the standard hadronic scenario, including magnetically powered corona models having hard spectra with $s_{\rm CR}\lesssim2$.

The James Webb Space Telescope (JWST) provides low- to medium-resolution spectra with unprecedented precision and broad near- to mid-infrared wavelength coverage, enabling detailed characterization of exoplanet atmospheres. We present a new JWST NIRISS SOSS transit observation of the warm sub-Saturn HAT-P-12b. Combined with NIRSpec G395M and MIRI LRS data, this enables an assessment of the information content across JWST instruments over the full accessible wavelength range. The NIRISS data were reduced and the impact of reduction choices on the transmission spectrum evaluated. Atmospheric retrievals were performed for all JWST combinations, with selected cases including archival HST data. Four molecules are significantly detected: H2O, CO2, CO, and H2S. Except for H2O, detections require NIRSpec coverage, while H2S is only detected in multi-instrument retrievals. NIRISS SOSS is essential to establish robust evidence for non-gray cloud behavior. A moderate scattering slope (p < 4) is consistently retrieved. Single-instrument retrievals tend to overestimate abundances, whereas combined JWST datasets yield more consistent constraints. The C/O ratio remains sensitive to differences between NIRSpec reductions. Results broadly agree with studies of WASP-39b, but highlight variations in information content across exoplanet types.

Radiation of X-ray pulsars is powered by accretion on the neutron star surface from a binary companion under the influence of a strong magnetic field. We study beaming of this radiation in the case of subcritical X-ray pulsars, where it is formed in the accretion channel close to the neutron star surface. We solve equations of the hydrodynamics and radiative transfer of two coupled polarization modes in the accretion channel numerically, taking into account resonant Compton scattering and vacuum polarization. The beaming patterns are obtained for different accretion rates, photon energies and polarizations, and for different models of the neutron star surface radiation. The calculated beaming patterns are converted into light curves for both the intensity and polarization, taking into account the effects of General Relativity. These beaming patterns and light curves are found to be strongly affected by the resonant Compton scattering for photon energies comparable with the electron cyclotron energy. In particular, the angular redistribution of radiation near the cyclotron resonance may reduce the light-curve modulation amplitude, which is consistent with observational indications of a suppressed pulsed fraction at these energies.

The thermodynamic resourcefulness of quantum channels primarily depends on their underlying causal structure and their ability to generate quantum correlations. We quantify this interplay within the resource theory of athermality for bipartite quantum channels in the presence of a side channel acting as memory, referred to as the resource theory of conditional athermality. For channels with trivial output Hamiltonians, we characterize the optimal one-shot rates for distilling the identity gate from a given channel, as well as the cost of simulating the channel using the identity gate, under conditional Gibbs-preserving superchannels. We show that these rates have a direct trade-off relation with the conditional channel entropies, attributing operational significance to signaling in quantum processes. Furthermore, we establish an equipartition property for the conditional channel min-entropy for classes of channels that are either tele-covariant or no-signaling from the non-conditioning input to the conditioning output. As a consequence, we demonstrate asymptotic reversibility of the resource theory for these channels. The asymptotic conditional athermality capacity of a tele-covariant channel is half the superdense coding capacity of its Choi state. Our work establishes the conditional channel entropy as a primitive information-theoretic concept for quantum processes, elucidating its potential for wider applications in quantum information science.

For first passage percolation (FPP) on Euclidean lattices $\mathbb{Z}^d$ with $d\ge 2$, it is expected that the variance of the first passage time between two points grows sublinearly in the distance with a universal exponent strictly smaller than $1$. Following Kesten's $O(n)$ upper bound (Ann. Appl. Probab., 1993) on the variance, Benjamini, Kalai and Schramm (Ann. Probab., 2003) used hypercontractivity to obtain an improvement of a factor of $\log n$ when passage times take two values with equal probability. This was later extended to more general classes of passage time distributions. However, unlike in exactly solvable planar models in last passage percolation where the variance is known to be $Θ(n^{2/3})$, the best known upper bound for the variance of passage times has remained $O(n/\log n)$ in all non-trivial variants of FPP. For a class of rotationally invariant Riemannian FPP on the plane, we show that the variance is $O(n^{1-\varepsilon})$ for some $\varepsilon>0$. Our argument uses fluctuation estimates for passage times and geodesics derived in Basu, Sidoravicius and Sly (2023) together with a multi-scale argument to establish that the geodesic exhibits disorder chaos, i.e., upon resampling a small fraction of the underlying randomness, the updated geodesic has on average a small overlap with the original one; this, established at a large number of scales, leads to a polynomial improvement of the variance bound.

We study the problem of controlling how a limited communication bandwidth budget is allocated across heterogeneously quantized sensor measurements. The performance criterion is the trace of the error covariance matrix of the linear minimum mean square error (LMMSE) state estimator, i.e., an $A$-optimal design criterion. Minimizing this criterion with a bit budget constraint yields a nonconvex optimization problem. We derive a formula that reduces each evaluation of the gradient to a single Cholesky factorization. This enables efficient optimization by both a projection-free Frank-Wolfe method (with a computable convergence certificate) and an interior point method with L-BFGS Hessian approximation over the problem's continuous relaxation. A largest remainder rounding procedure recovers integer bit allocations with a bound on the quality of the rounded solution. Numerical experiments in IEEE power grid test cases with up to 300 buses compare both solvers and demonstrate that the analytic gradient is the key computational enabler for both methods. Additionally, the heterogeneous bit allocation is compared to standard uniform bit allocation on the 500 bus IEEE power grid test case.

Regularity theorems à la Avellaneda-Lin are an indispensable part of the modern quantitative theory of stochastic homogenization. While interior regularity results for random elliptic operators have been available for a while, on general smooth domains the existing theory has until recently remained limited to Lipschitz estimates. We establish $C^{1,α}$ regularity results for random elliptic operators on bounded sufficiently smooth domains, as well as for scalar problems on convex polytopes. We, furthermore, prove a number of auxiliary results typically employed in the derivation of fluctuation bounds, such as a weighted Meyers estimate.

To a noncompact orientable surface with no closed boundary, we associate the sum of Fukaya categories of (Liouville sectors associated to) its symmetric powers. We construct sectorial covers with the combinatorics of the bar resolution to show this association extends to an open 2d topological field theory -- without naming a Lagrangian, let alone a holomorphic disk. In particular, we recover results of Rouquier and Manion on extending Heegaard-Floer theory down to an interval.

Quantum phase estimation is a central primitive in quantum algorithms and sensing, where performance is governed by the sensitivity of measurement signals to the target parameter. While existing methods have developed increasingly sophisticated inference and adaptive design strategies, the signal family used for phase learning is often largely pre-specified. Here we propose a programmable signal design framework for quantum phase estimation based on quantum signal processing, which enables the measurement signal to be tailored to the current uncertainty region. We cast phase estimation as a max-min optimization problem over admissible signals and introduce a sensitivity efficiency parameter that quantifies information gain per query depth. The resulting iterative algorithm combines optimized quantum signal transformations with structured classical inference, retaining Heisenberg-limited scaling while improving sensitivity efficiency and practical resource prefactors. Numerical results show reduced estimation variance compared with standard protocols such as robust phase estimation. Our framework also extends to Hamiltonian eigenvalue estimation in higher dimensions and establishes a quantum-classical co-design paradigm through programmable signal shaping.

We develop reliable a posteriori error estimators for fully discrete Runge-Kutta discontinuous Galerkin approximations of nonlinear convection-diffusion systems endowed with a convex entropy in multiple spatial dimensions on the flat torus T^d, with a focus on the convection-dominated regime. In order to use the relative entropy method, we reconstruct the numerical solution via tensor-product Smoothness-Increasing Accuracy-Conserving (SIAC) filtering which has superconvergence properties. We then derive reliable a posteriori error estimators for the difference between the entropy weak solution and the reconstruction, with constants that are uniform in the vanishing viscosity limit. Our numerical experiments show that the a posteriori error bounds converge with the same order as the error of the reconstructed numerical solution.

Recently, two independent research efforts have been made to study the stochastic Galerkin formulation of the shallow water equations. %In particular, Bender and Öffner developed entropy-conservative discontinuous Galerkin (DG) methods to solve the stochastic shallow water equations in an stochastic Galerkin framework using Roe variable transformation, while Dai, Epshteyn and collaborators proposed second-order, energy-stable and well-balanced schemes for the same class of problems with a specific projection step used inside the Galerkin projection together with high-order quadrature rules and a time-step restriction. In this paper, we provide a comprehensive comparison of the two methodologies mentioned, focusing on their theoretical properties and practical implementation aspects. We highlight shared foundational concepts and key differences of both approaches, with a particular focus on the selection of basis functions in the stochastic domain. As a highlight, we show that under specific conditions, the two formulations align, offering a unified framework that connects these distinct approaches. From our theoretical findings, we extend the development of high-order entropy conservative DG methods for the one-dimensional stochastic Galerkin shallow equations to two space dimensions; constructing entropy conservative two-point fluxes via primitive variables instead of entropy variables and applying it in our high-order DG setting. In numerical simulations, we verify and support our theoretical findings of a well-balanced and entropy-stable DG scheme which can be used to solve geophyiscal fluid flows with uncertainty.

Radio flares have been postulated to be associated with the production of astrophysical neutrinos. For example, TXS 0506+056 exhibits a 2-3 yr delay between the 2017 IceCube-170922A/$γ$-ray flare and a GHz radio maximum. We quantitatively test if the delayed radio flare originates from the same compact region where neutrinos and $γ$-rays are produced as it expands downstream and synchrotron self-absorption (SSA) is reduced. Starting from the 2017 flare blob parameters, we model the expanding production region and its evolving radio emission with LeHaMoC in a fully time-dependent framework, and compare our 1.2-22 GHz light curves to RATAN-600 data. We study different scenarios with increasing levels of sophistication, including continuous injection and energy re-dissipation on pc scales. While a simple expanding blob scenario fails to reproduce the radio data, a downstream dissipation episode of particles in the optically thin regime, followed by jet deceleration, successfully describes the radio evolution. Within our one-zone time-dependent framework, the delayed radio flare is unlikely to come from an expanding neutrino production zone becoming transparent to radio emission. Additional ingredients are needed, such as re-dissipation downstream with a subsequent Doppler-factor decline. The radio flare is powered by leptonic synchrotron emission and is largely insensitive to the proton population relevant for neutrino production, implying that the delayed radio flare mainly probes downstream dissipation and beaming in certain jet configurations rather than being a genuine feature associated with the neutrino production.

Large language models (LLMs) and their applications, such as agents, are highly vulnerable to prompt injection attacks. State-of-the-art prompt injection detection methods have the following limitations: (1) their effectiveness degrades significantly as context length increases, and (2) they lack explicit rules that define what constitutes prompt injection, causing detection decisions to be implicit, opaque, and difficult to reason about. In this work, we propose AgentWatcher to address the above two limitations. To address the first limitation, AgentWatcher attributes the LLM's output (e.g., the action of an agent) to a small set of causally influential context segments. By focusing detection on a relatively short text, AgentWatcher can be scalable to long contexts. To address the second limitation, we define a set of rules specifying what does and does not constitute a prompt injection, and use a monitor LLM to reason over these rules based on the attributed text, making the detection decisions more explainable. We conduct a comprehensive evaluation on tool-use agent benchmarks and long-context understanding datasets. The experimental results demonstrate that AgentWatcher can effectively detect prompt injection and maintain utility without attacks. The code is available at https://github.com/wang-yanting/AgentWatcher.

We develop a rigorous and implementable framework for Gibbs sampling of infinite-dimensional quantum systems governed by unbounded Hamiltonians. Extending dissipative Gibbs samplers beyond finite dimensions raises fundamental obstacles, including ill-defined generators, the absence of spectral gaps on natural Banach spaces, and tensions between implementability and convergence guarantees. We overcome these issues by constructing KMS-symmetric quantum Markov semigroups on separable Hilbert spaces that are both well-posed and efficiently implementable on qubit hardware. Our generation theory is based on the abstract framework of Dirichlet forms, adapted here to the case of algebras of bounded operators over separable Hilbert spaces. Leveraging the spectral properties of our self-adjoint generators, we establish quantitative convergence results in trace distance, including regimes of fast thermalization. In contrast, we also identify Hamiltonians for which a naive choice of generators guaranteeing implementability generally comes at the cost of losing convergence of the associated evolutions, thereby establishing a strong trade-off between implementability and convergence. Our framework applies to a wide class of models, including Schrödinger operators, Gaussian systems, and Bose-Hubbard Hamiltonians, and provides a unified approach linking rigorous infinite-dimensional analysis with algorithmic Gibbs state preparation.

Recently, a version of the deformation method developed in arXiv:2104.07816 has been used to great effect to compute the local zeta functions of Calabi-Yau threefolds by computing their periods as series with rational coefficients and using this to find a matrix representing the Frobenius action on a $p$-adic cohomology. However, this method rapidly becomes inefficient as the prime $p$ grows, due to the rational period coefficients growing quickly. In this paper, we point out that this problem can be circumvented by a simple process that we call $p$-adically truncated recurrence. This is a recurrence relation whose solutions are $p$-adic numbers modulo $p^A$ for a given $A \in \mathbb{N}$ and thus grow only slowly as $p$ grows. We show that the $p$-adic accuracy $A$ can be chosen such that all $p$-adic digits which contribute to the final result are kept, and therefore we are able to obtain the correct result by using these solutions. The improvements to speed and memory usage allow for computing the local zeta functions for tens of thousands of primes on a desktop computer, and make computing local zeta functions possible even for primes of size $10^6$ to $10^7$. Previously such computations were practically possible for around 1000 first primes. We have implemented this method in a Sage-compatible Python package PFLFunction.

We obtain bivariate asymptotics for one part monotone Hurwitz numbers in high genus (i.e. as both the size and the genus go to infinity). To do so, we start with a linear recurrence for these numbers obtained by Do and Chaudhuri. Then, we apply a recent method developped by Elvey-Price, Fang, Wallner and the second author to extract asymptotics from such recurrences.