Retrieval-Augmented Generation (RAG) is an emerging approach in natural language processing that combines large language models (LLMs) with external document retrieval to produce more accurate and grounded responses. While RAG has shown strong potential in reducing hallucinations and improving factual consistency, it also introduces new privacy and security challenges that differ from those faced by traditional LLMs. Existing research has demonstrated that LLMs can leak sensitive information through training data memorization or adversarial prompts, and RAG systems inherit many of these vulnerabilities. At the same time, reliance of RAG on an external knowledge base opens new attack surfaces, including the potential for leaking information about the presence or content of retrieved documents, or for injecting malicious content to manipulate model behavior. Despite these risks, there is currently no formal framework that defines the threat landscape for RAG systems. In this paper, we address a critical gap in the literature by proposing, to the best of our knowledge, the first formal threat model for retrieval-RAG systems. We introduce a structured taxonomy of adversary types based on their access to model components and data, and we formally define key threat vectors such as document-level membership inference and data poisoning, which pose serious privacy and integrity risks in real-world deployments. By establishing formal definitions and attack models, our work lays the foundation for a more rigorous and principled understanding of privacy and security in RAG systems.

Flow-based generative models can face numerical challenges on scientific data with multiscale Fourier spectra, often producing large errors at fine scales. We approach this problem within the flow matching and stochastic interpolants framework, through the principled design of noise distributions and interpolation schedules. Working in function space ensures that the generative model remains well defined as the resolution is refined; the Lipschitz regularity of the drift is important to both this function-space well-posedness and the integration cost at fixed resolution. The central observation is that the noise should be at least as rough as the target distribution -- measured by Fourier-spectrum decay -- in order to keep the Lipschitz constant finite. For Gaussian and near-Gaussian targets whose fine-scale structure is known, matched-spectrum noise improves numerical efficiency over standard white-noise choices. For more complex non-Gaussian targets, matched-spectrum noise may not be sufficient, and we propose scale-adaptive interpolation schedules to mitigate the terminal-time stiffness that arises when the noise is rougher than the data. Numerical experiments on synthetic Gaussian random fields and on invariant measures of the stochastic Allen--Cahn and Navier--Stokes equations illustrate the approach and demonstrate its ability to generate high-fidelity samples at lower computational cost than traditional approaches.

Ontologies and taxonomies of research fields are critical for managing and organising scientific knowledge, as they facilitate efficient classification, dissemination and retrieval of information. However, the creation and maintenance of such ontologies are expensive and time-consuming tasks, usually requiring the coordinated effort of multiple domain experts. Consequently, ontologies in this space often exhibit uneven coverage across different disciplines, limited inter-discipline connectivity, and infrequent updating cycles. In this study, we investigate the capability of several large language models to identify semantic relationships among research topics within three academic disciplines: biomedicine, physics, and engineering. The models were evaluated under three distinct conditions: zero-shot prompting, chain-of-thought prompting, and fine-tuning on existing ontologies. Additionally, we assessed the cross-discipline transferability of fine-tuned models by measuring their performance when trained in one discipline and subsequently applied to a different one. To support this analysis, we introduce PEM-Rel-8K, a novel dataset consisting of over 8,000 relationships extracted from the most widely adopted taxonomies in the three disciplines considered in this study: MeSH, PhySH, and IEEE. Our experiments demonstrate that fine-tuning LLMs on PEM-Rel-8K yields excellent performance across all disciplines.

This study investigates the pre-trained RNN attention models with the mainstream attention mechanisms, such as additive attention, Luong's three attentions, global self-attention and sliding window sparse attention, for the empirical asset pricing research on the top 420 large-cap US stocks. This is the first paper on the large-scale state-of-the-art (SOTA) attention mechanisms applied in the asset pricing context. They overcome the limitations of the traditional machine learning-based asset pricing, such as mis-capturing the temporal dependency and short memory. Moreover, the enforced causal masks in the attention mechanisms address the future data leaking issue ignored by the more advanced attention-based models, such as the classic Transformer. The proposed attention models also consider the temporal sparsity characteristic of asset pricing data and mitigate potential overfitting issues by deploying the simplified model structures. This provides some insights for future empirical economic research. All models are examined in three periods, which cover pre-COVID-19, COVID-19 and one year post-COVID-19, for testing the stability of these models under extreme market conditions. The study finds that in value-weighted portfolio back testing, the global self-attention model and the sliding window sparse attention model exhibit excellent capabilities in deriving the absolute returns and hedging downside risks, while they achieve an annualized Sortino ratio of 2.0 and 1.80 respectively in the period with COVID-19 in the static transaction cost scenario. Moreover, the sliding window sparse attention model performs more stably than the global self-attention model from the perspective of absolute portfolio returns with respect to the size of stocks' market capitalization.

In this study, we extend the contrast source inversion to a fully differentiable, unsupervised framework based on a neural implicit representation of the contrast source. Specifically, instead of a pixel-wise discrete representation, the contrast source is parameterized by a lightweight residual multilayer perceptron (ResMLP) as a continuous neural field conditioned on spatial coordinates and transmitter settings. This continuous parameterization provides a more flexible representation of the contrast source and improves reconstruction accuracy and robustness under noisy measurements. Building on this representation, the state equation and data equation are combined with total-variation regularization to form a differentiable objective function. By reformulating the VIE-constrained inversion as an end-to-end differentiable optimization problem, the network parameters and the medium contrast are jointly optimized via automatic differentiation. Within the same framework, both full and phaseless data inversion are accommodated by only modifying the data misfit function. Numerical experiments demonstrate that this scheme yields higher reconstruction accuracy and robustness than conventional CSI across a range of noise levels and measurement settings. The continuous neural field further enables super-resolution inference at resolutions finer than the training grid, decoupling inversion cost from reconstruction fidelity. Ablation studies and comparisons with alternative neural architectures further confirm that the contrast source parameterization and VIE-based formulation are both essential to the observed improvements.

The design of many classical optimization algorithms is driven by the certification of linear convergence rates over classes of optimization problems. In this paper, we consider the problem of improving the average-case performance of an algorithm over a specific distribution of problem instances. While this task can be tackled by embedding trainable components into the algorithm updates, a key challenge is to preserve worst-case guarantees across the entire problem class. For classes of composite optimization problems, we show that all linearly convergent algorithms can be parametrized in terms of a baseline linearly convergent algorithm, and a set of trainable, exponentially-decaying modifications to its update rule; crucially, this parametrization excludes all-and only-the algorithms that do not converge linearly. Our results apply to improving the average-case performance of classical algorithms such as gradient descent for nonconvex, gradient-dominated functions; Nesterov's accelerated method for smooth, strongly convex functions; and projected gradient methods for optimization over polyhedral feasible sets. We illustrate how our characterization can be used for learning to optimize with linear convergence and feasibility guarantees. Numerical results showcase benefits over classical optimizers when solving ill-conditioned systems of linear equations and running a model predictive control scheme on a linear dynamical system.

We study the optimization of non-convex functions that are not necessarily smooth (gradient and/or Hessian are Lipschitz) using first order methods. Smoothness is a restrictive assumption in machine learning in both theory and practice, motivating significant recent work on finding first order stationary points of functions satisfying generalizations of smoothness with first order methods. We develop a novel framework that lets us systematically study the convergence of a large class of first-order optimization algorithms (which we call decrease procedures) under generalizations of smoothness. We instantiate our framework to analyze the convergence of first order optimization algorithms to first and \textit{second} order stationary points under generalizations of smoothness. As a consequence, we establish the first convergence guarantees for first order methods to second order stationary points under generalizations of smoothness. We demonstrate that several canonical examples fall under our framework, and highlight practical implications.

Federated learning transmits only model updates to protect client data, and differentially private SGD (DP-SGD) bounds content-level leakage through those updates. Neither mechanism accounts for what the communication topology of the federation itself reveals. In cross-silo deployments, a passive adversary with knowledge of the topology and organisational structure has access to information channels that DP-SGD leaves entirely unaddressed. We formalise this threat and derive a principled defense. We introduce TADI (Topology-Aware Distributional Inference), a shadow-trained channel decomposition that isolates per-client leakage into parameter, structural, and organisational components via four channel ablations, and prove an additive per-client mutual-information bound separating a controllable mechanism term from an uncontrollable prior-coupling floor. From this bound we derive Fulcrum, a closed-form balanced min-max optimal noise allocation that strictly dominates uniform DP-SGD whenever the federation's leverage profile is asymmetric, and degenerates exactly to uniform DP-SGD when it is not, making it safe to adopt unconditionally. Evaluated on Fed-ISIC2019, Fed-Heart-Disease, and synthetic CIFAR-10 across six topology families, Fulcrum delivers privacy gains of up to 1.967 nats at no measurable utility cost. The TADI channel decomposition confirms that the parameter channel is bounded by DP-SGD across all settings, the prior-coupling channel is empirically attained under matched-prior conditions, and the bound is conservative in a deployment-favourable direction under realistic cross-silo threat models.

Recent advances in generative artificial intelligence (GenAI) models have enabled the generation of personalized content that adapts to up-to-date user context. While personalized decision systems are often modeled using bandit formulations, the integration of GenAI introduces new structure into otherwise classical sequential learning problems. In GenAI-powered interventions, the agent selects a query, but the environment experiences a stochastic response drawn from the generative model. Standard bandit methods do not explicitly account for this structure, where actions influence rewards only through stochastic, observed treatments. We introduce generator-mediated bandit-Thompson sampling (GAMBITTS), a bandit approach designed for this action/treatment split, using mobile health interventions with large language model-generated text as a motivating case study. GAMBITTS explicitly models both the treatment and reward generation processes, using information in the delivered treatment to accelerate policy learning relative to standard methods. We establish regret bounds for GAMBITTS by decomposing sources of uncertainty in treatment and reward, identifying conditions where it achieves stronger guarantees than standard bandit approaches. In simulation studies, GAMBITTS consistently outperforms conventional algorithms by leveraging observed treatments to more accurately estimate expected rewards.

Urban air pollution hotspots pose significant health risks, yet their detection and analysis remain limited by the sparsity of public sensor networks. This paper addresses this challenge by combining predictive modeling and mechanistic approaches to comprehensively monitor pollution hotspots. We enhanced New Delhi's existing sensor network with 28 low-cost sensors, collecting PM2.5 data over 30 months from May 1, 2018, to Nov 1, 2020. Applying established definitions of hotspots to this data, we found the existence of additional 189 hidden hotspots apart from confirming 660 hotspots detected by the public network. Using predictive techniques like Space-Time Kriging, we identified hidden hotspots with 95% precision and 88% recall with 50% sensor failure rate, and with 98% precision and 95% recall with 50% missing sensors. The projected results of our predictive models were further compiled into policy recommendations for public authorities. Additionally, we developed a Gaussian Plume Dispersion Model to understand the mechanistic underpinnings of hotspot formation, incorporating an emissions inventory derived from local sources. Our mechanistic model is able to explain 65% of observed transient hotspots. Our findings underscore the importance of integrating data-driven predictive models with physics-based mechanistic models for scalable and robust air pollution management in resource-constrained settings.

Compared to other clinical screening techniques, speech-and-language-based automated Alzheimer's disease (AD) detection methods are characterized by their non-invasiveness, cost-effectiveness, and convenience. Previous studies have demonstrated the efficacy of fine-tuning pre-trained language models (PLMs) for AD detection. However, the objective of this traditional fine-tuning method, which involves inputting only transcripts, is inconsistent with the masked language modeling (MLM) task used during the pre-training phase of PLMs. In this paper, we investigate prompt-based fine-tuning of PLMs, converting the classification task into a MLM task by inserting prompt templates into the transcript inputs. We also explore the impact of incorporating pause information from forced alignment into manual transcripts. Additionally, we compare the performance of various automatic speech recognition (ASR) models and select the Whisper model to generate ASR-based transcripts for comparison with manual transcripts. Furthermore, majority voting and ensemble techniques are applied across different PLMs (BERT and RoBERTa) using different random seeds. Ultimately, we obtain maximum detection accuracy of 95.8% (with mean 87.9%, std 3.3%) using manual transcripts, achieving state-of-the-art performance for AD detection using only transcripts on the ADReSS test set.

In Federated Learning, it is crucial to handle low-quality, corrupted, or malicious data. However, traditional data valuation methods are not suitable due to privacy concerns. To address this, we propose a simple yet effective approach that utilizes a new influence approximation called "lazy influence" to filter and score data while preserving privacy. To do this, each participant uses their own data to estimate the influence of another participant's batch and sends a differentially private obfuscated score to the central coordinator. Our method has been shown to successfully filter out biased and corrupted data in various simulated and real-world settings, achieving a recall rate of over $>90\%$ (sometimes up to $100\%$) while maintaining strong differential privacy guarantees with $\varepsilon \leq 1$.

In this paper we contribute to the frequently studied question of how to decompose a continuous piecewise linear (CPWL) function into a difference of two convex CPWL functions. Every CPWL function has infinitely many such decompositions, but for applications in optimization and neural network theory, it is crucial to find decompositions with as few linear pieces as possible. This is a highly challenging problem, as we further demonstrate by disproving a recently proposed approach by Tran and Wang [Minimal representations of tropical rational functions. Algebraic Statistics, 15(1):27-59, 2024]. To make the problem more tractable, we propose to fix an underlying polyhedral complex determining the possible locus of nonlinearity. Under this assumption, we prove that the set of decompositions forms a polyhedron that arises as intersection of two translated cones. We prove that irreducible decompositions correspond to the bounded faces of this polyhedron and minimal solutions must be vertices. We then identify cases with a unique minimal decomposition, and illustrate how our insights have consequences in the theory of submodular functions. Finally, we improve upon previous constructions of neural networks for a given convex CPWL function and apply our framework to obtain results in the nonconvex case.

Understanding spatial relationships across all dimensions is fundamental for intelligent systems. However, existing positional embeddings, such as Rotary Positional Embedding (RoPE), lack theoretical guarantees for high-dimensional spatiotemporal tasks like video understanding and robotic navigation. Inspired by the hexagonal periodic coding of grid cells in mammalian spatial cognition, we propose GridPE -- a novel positional embedding framework that integrates computational neuroscience principles with harmonic analysis. Our approach builds upon Random Fourier Features and leverages principles from neuroscience to construct efficient embeddings. Theoretically, we prove that any translation-invariant spatial function can be approximated by a finite sum of Fourier bases, which naturally reduces to RoPE in the one-dimensional case. We then derive the directions and quantities of frequency vectors at each scale in any Euclidean dimension, along with the optimal ratio between different scales, from a bioavailability perspective. These derivations are equivalent to the relationship between the centroid and the vertices of a regular simplex in that dimension. We validate GridPE across a range of spatial modeling tasks, including 2D image classification (ImageNet100) and 3D point cloud recognition (ModelNet40). Our theoretical analysis establishes GridPE as a unified framework for positional embedding in arbitrary-dimensional spaces, while empirical results demonstrate its superiority over existing methods.

Only a small fraction of patients with chronic kidney disease (CKD) progress to dialysis, creating severe class imbalance that limits the performance of machine learning models for early dialysis prediction. This challenge is compounded by the binary structure of electronic health record (EHR) data, for which most existing augmentation methods were not designed. We propose Binary Gaussian Copula Synthesis (BGCS), a two-stage data augmentation method tailored to binary clinical data. BGCS first generates synthetic minority-class samples using a Gaussian copula framework that explicitly models pairwise dependencies among binary features, then applies a fine-tuned GPT-2 classifier to filter out clinically implausible samples before training. We evaluated BGCS on a real-world EHR dataset of 15,169 patients with CKD from West Virginia collected between 2008 and 2022, benchmarking it against SMOTE, CTGAN, and standard Gaussian Copula across four machine learning classifiers over 25 independent runs. BGCS consistently outperformed all comparison methods, achieving the highest minority-class recall for 90-day dialysis prediction, with median values ranging from 0.78 to 0.87 across classifiers, and the strongest distributional fidelity to real data, with a mean p-value of 0.68 across features. The best-performing BGCS-augmented model was integrated into an interpretable decision tree-based clinical decision support system for dialysis risk stratification, with electrolyte imbalances, cardiovascular comorbidities, and renal monitoring indicators emerging as the most influential predictive features. These findings suggest that augmentation methods designed for the structural properties of binary EHR data can meaningfully improve early dialysis risk prediction and support the development of interpretable clinical decision-support tools for CKD care.

Background. Coronary artery calcium (CAC) is a powerful predictor of major adverse cardiovascular events (MACE). Traditional Agatston score simply sums the calcium, albeit in a non-linear way, leaving room for improved calcification assessments that will more fully capture the extent of disease. Objective. To determine if AI methods using detailed calcification features (i.e., calcium-omics) can improve MACE prediction. Methods. We investigated additional features of calcification including assessment of mass, volume, density, spatial distribution, territory, etc. We used a Cox model with elastic-net regularization on 2457 CT calcium score (CTCS) enriched for MACE events obtained from a large no-cost CLARIFY program (ClinicalTri-als.gov Identifier: NCT04075162). We employed sampling techniques to enhance model training. We also investigated Cox models with selected features to identify explainable high-risk characteristics. Results. Our proposed calcium-omics model with modified synthetic down sampling and up sampling gave C-index (80.5%/71.6%) and two-year AUC (82.4%/74.8%) for (80:20, training/testing), respectively (sampling was applied to the training set only). Results compared favorably to Agatston which gave C-index (71.3%/70.3%) and AUC (71.8%/68.8%), respectively. Among calcium-omics features, numbers of calcifications, LAD mass, and diffusivity (a measure of spatial distribution) were important determinants of increased risk, with dense calcification (>1000HU) associated with lower risk. The calcium-omics model reclassified 63% of MACE patients to the high risk group in a held-out test. The categorical net-reclassification index was NRI=0.153. Conclusions. AI analysis of coronary calcification can lead to improved results as compared to Agatston scoring. Our findings suggest the utility of calcium-omics in improved prediction of risk.

Current methods for determining whether a time series exhibits fractal structure (FS) rely on subjective assessments on estimators of the Hurst exponent (H). Here, I introduce the Bayesian Assessment of Scaling, an analytical framework for drawing objective and accurate inferences on the FS of time series. The technique exploits the scaling property of the diffusion associated to a time series. The resulting criterion is simple to compute and represents an accurate characterization of the evidence supporting different hypotheses on the scaling regime of a time series. Additionally, a closed-form Maximum Likelihood estimator of H is derived from the criterion, and this estimator outperforms the best available estimators.

Pharmaceutical supply chains (PSCs) struggle with inventory management (IM) due to unpredictable demand patterns and variable lead times associated with restocking. This complexity is further compounded by the finite shelf lives of pharmaceutical products, which necessitate a delicate balance between adequate stock and minimal waste. These intertwined factors create a complex optimization problem that requires sophisticated inventory strategies to ensure both product availability and PSC efficiency. This study aims to develop an optimal inventory replenishment policy for pharmaceutical products that can handle the stochasticity arising from uncertain demand and variable PSC conditions. The objective is to maximize the profitability of the PSC while maintaining a high patient service level. We formulate the problem as a Markov decision process and propose a deep reinforcement learning (DRL) approach, specifically, a hybrid asynchronous advantage actor critic distributed proximal policy optimization (A3C DPPO)algorithm. The A3C DPPO algorithm is tailored to handle the continuous action space inherent in IM. The numerical results demonstrate that the proposed algorithm adaptively updates the inventory replenishment strategy under dynamic scenarios, resulting in lower inventory costs compared to various benchmarks. We also conduct numerical validation using real-world pharmaceutical inventory data to confirm the practical feasibility of the proposed algorithm.

Sow body condition is an important indicator for growers as it has a large impact on lactation performance and piglet survival. However, body condition measures used during production, such as visual scoring and calipers, correlate poorly with underlying tissue composition. Ultrasound scans can provide direct measurements of subcutaneous backfat thickness and loin muscle depth, but their operation is labor intensive and not scalable for production. We present PigFormer, an end-to-end two-stage system that takes raw depth frames from a ceiling-mounted RGB-D camera and predicts subcutaneous backfat thickness, loin muscle depth, and total tissue thickness at the last rib. Stage 1 is a geometric front-end that converts raw depth into a standardized height map via SAM3-to-MaskDINO segmentation distillation, ground-plane removal, and orientation normalization. Stage 2 is a Slice Attention Encoder that treats each height map as a sequence of cross-sectional slices and captures spatial relationships along the full dorsal surface. On a multi-site dataset of 319 sow and gilt instances from two facilities, PigFormer achieves 2.43 mm backfat MAE and 3.87 mm overall MAE. It outperforms strong single-stage ResNet-18 and ViT-small baselines. PigFormer offers a practical path toward continuous, automated, non-contact body condition monitoring in commercial swine production. Code is available at https://github.com/iambashar/Pigformer.

Reinforcement learning has long struggled with poor sample efficiency. One promising approach to mitigate this problem is leveraging group-invariant Markov Decision Processes ($G$-invariant MDPs). Existing works in this direction have primarily focused on image-based RL and rotational symmetry such as $\mathrm{SO(2)}$, leaving state-based RL and reflection symmetry largely underexplored. In this work, we focus on state-based continuous control tasks and exploit reflection symmetry by introducing Reflex, a paradigm that seamlessly integrates with both on-policy and off-policy RL algorithms. We formalize two types of reflection-axial reflection and bilateral reflection, and characterize their corresponding transformations. Building on a theoretical analysis of symmetry-preserving optimal value functions and policies, Reflex integrates reflection symmetry into policy learning through principled symmetry regularization mechanisms. We integrate Reflex with PPO and SAC, and evaluate it on a suite of OpenAI Gym and DeepMind Control benchmarks, demonstrating superior performance over standard baselines while improving sample efficiency. Our code is available at https://github.com/TonyStark042/Reflex.

Self-generated counterfactual explanations (SCEs) are minimally modified inputs (minimality) generated by large language models (LLMs) that flip their own predictions (validity), offering a causally grounded approach to unraveling black-box LLM behavior. Yet extending them beyond English remains challenging: existing methods struggle to produce valid SCEs in non-dominant languages, and a persistent trade-off between validity and minimality undermines explanation quality. We introduce Macro, a preference alignment framework that applies Direct Preference Optimization (DPO) to multilingual SCE generation, using a composite scoring function to construct preference pairs that effectively translate the trade-off into measurable preference signals. Experiments across four LLMs and seven typologically diverse languages show that Macro improves validity by 12.55\% on average over the chain-of-thought baseline without degrading minimality, while avoiding the severe minimality violations of the translation-based baseline. Compared to supervised fine-tuning, Macro achieves superior performance on both metrics, confirming that explicit preference optimization is essential for balancing this trade-off. Further analyses reveal that Macro increases cross-lingual perturbation alignment and mitigates common generation errors. Our results highlight preference optimization as a promising direction for enhancing multilingual model explanations.

Large Language Models (LLMs) have demonstrated strong capabilities in natural language understanding and reasoning, while recent extensions that incorporate visual inputs enable them to process multimodal information. Despite these advances, Large Vision-Language Models (LVLMs) incur substantial computational and memory costs, hindering deployment in resource-constrained scenarios. Existing layer pruning methods typically rely on local similarity metrics or static proxy signals, failing to capture the global and dynamic evolution of representations across model depth, which often leads to the removal of transition-critical layers. To address this limitation, we propose a topology-aware layer pruning framework for LVLMs. Specifically, we represent layer wise hidden states as point clouds and models their evolution using \textit{simplicial complexes}. By leveraging \textit{zigzag persistent homology}, we quantify inter-layer topological consistency and enable adaptive pruning that preserves critical representational transitions. Extensive experiments on diverse multimodal benchmarks demonstrate that the proposed framework consistently outperforms existing pruning methods across a wide range of sparsity ratios. Our code is available at https://github.com/zpc456/TopoVLM.

Reservoir simulation workflows face a fundamental data asymmetry: input parameter fields (geostatistical permeability realizations, porosity distributions) are free to generate in arbitrary quantities, yet existing neural operator surrogates require large corpora of expensive labeled simulation trajectories and cannot exploit this unlabeled structure. We introduce \textbf{PI-JEPA} (Physics-Informed Joint Embedding Predictive Architecture), a surrogate pretraining framework that trains \emph{without any completed PDE solves}, using masked latent prediction on unlabeled parameter fields under per-sub-operator PDE residual regularization. The predictor bank is structurally aligned with the Lie--Trotter operator-splitting decomposition of the governing equations, dedicating a separate physics-constrained latent module to each sub-process (pressure, saturation transport, reaction), enabling fine-tuning with as few as 100 labeled simulation runs. On single-phase Darcy flow, PI-JEPA achieves $1.9\times$ lower error than FNO and $2.4\times$ lower error than DeepONet at $N_\ell{=}100$, with 24\% improvement over supervised-only training at $N_\ell{=}500$, demonstrating that label-free surrogate pretraining substantially reduces the simulation budget required for multiphysics surrogate deployment.

This paper proposes a measurement standardisation framework that compresses expert-AI interactions into structured, comparable fields for prospective risk detection in deployed AI systems, without access to model internals. The main aim of this concept paper is to define the scope of the framework, both semantically and statistically, and to specify a protocol for its empirical testing in future work. The population-level claims the framework is designed to support are therefore the subject of a staged research programme rather than results claimed in this paper. Measurement standardisation underpins all three claims that follow. The first is a reliability claim: under bounded conditions, large language models can produce reliable, standardised assessments of the evidential and policy alignment of expert-AI interactions. The second is a governance claim: alignment scores give experts an immediate signal during deployment and give institutions a basis for monitoring alignment patterns across mission types, models, and domains. The third is an epidemiological claim: once measurement standardisation is established, aggregate alignment scores could be used to study associations with downstream outcomes in regulated professional settings. This introduces the possibility of an "AI epidemiology" that detects risk based on correlated variables instead of mechanistic analysis. This paper addresses the first claim and specifies protocols for investigating the second and third. To enable empirical evaluation in future studies, this paper sets out a defined grammar, together with a statistical protocol based on paired bootstrap inference, DeLong's test for paired AUCs as a sensitivity check, a pre-specified one-sided non-inferiority margin of 0.05, and Holm-Bonferroni correction.

Open Large Language Model (LLM) benchmarks, such as HELM and BIG-Bench, provide standardized and transparent evaluation protocols that support comparative analysis, reproducibility, and systematic progress tracking in Language Model (LM) research. Yet, this openness also creates substantial risks of data leakage during LM testing--deliberate or inadvertent, thereby undermining the fairness and reliability of leaderboard rankings and leaving them vulnerable to manipulation by unscrupulous actors. We illustrate the severity of this issue by intentionally constructing cheating models: smaller variants of BART, T5, and GPT-2, fine-tuned directly on publicly available test-sets. As expected, these models excel on the target benchmarks but fail terribly to generalize to comparable unseen testing sets. We then examine task specific simple paraphrase-based safeguarding strategies to mitigate the impact of data leakage and evaluate their effectiveness and limitations. Our findings underscore three key points: (i) high leaderboard performance on limited open, static benchmarks may not reflect real-world utility; (ii) private or dynamically generated benchmarks should complement open benchmarks to maintain evaluation integrity; and (iii) a reexamination of current benchmarking practices is essential for reliable and trustworthy LM assessment.

Facial Emotion Analysis (FEA) extends traditional facial emotion recognition by incorporating explainable, fine-grained reasoning. The task integrates three subtasks: emotion recognition, facial Action Unit (AU) recognition, and AU-based emotion reasoning to model affective states jointly. While recent approaches leverage Vision-Language Models (VLMs) and achieve promising results, they face two critical limitations: (1) hallucinated reasoning, where VLMs generate plausible but inaccurate explanations due to insufficient emotion-specific knowledge; and (2) misalignment between emotion reasoning and recognition, caused by fragmented connections between observed facial features and final labels. We propose Facial-R1, a three-stage alignment framework that effectively addresses both challenges with minimal supervision. First, we employ instruction fine-tuning to establish basic emotional reasoning capability. Second, we introduce reinforcement training guided by emotion and AU labels as reward signals, which explicitly aligns the generated reasoning process with the predicted emotion. Third, we design a data synthesis pipeline that iteratively leverages the prior stages to expand the training dataset, enabling scalable self-improvement of the model. Built upon this framework, we introduce FEA-20K, a benchmark dataset comprising 17,737 training and 1,688 test samples with fine-grained emotion analysis annotations. Extensive experiments across eight standard benchmarks demonstrate that Facial-R1 achieves state-of-the-art performance in FEA, with strong generalization and robust interpretability.

We investigate the approximation of solution operators for partial differential equations (PDEs) using sparse high-dimensional techniques. Building on a dimension-incremental framework, we combine product basis expansions with sparse recovery methods, specifically orthogonal matching pursuit (OMP), to substantially reduce the required sample size compared with a previously considered cubature-based approach. We evaluate the resulting method numerically on several examples, comparing it against both cubature-based sparse approximation and Fourier neural operators in terms of accuracy, runtime, and sample size. The experiments show that our approach considerably reduces the number of required PDE solves relative to its predecessor while maintaining competitive accuracy, particularly when the solution admits a sparse representation in the chosen basis. Furthermore, the recovered sparse index sets yield interpretable insights into the relevant variables and parameter interactions.

We present Geodesic Semantic Search (GSS), a retrieval system that learns node-specific Riemannian metrics on citation graphs to enable geometry-aware semantic search. Unlike standard embedding-based retrieval that relies on fixed Euclidean distances, \gss{} learns a low-rank metric tensor $\mL_i \in \R^{d \times r}$ at each node, inducing a local positive semi-definite metric $\mG_i = \mL_i \mL_i^\top + \eps \mI$. This parameterization guarantees valid metrics while keeping the model tractable. Retrieval proceeds via multi-source Dijkstra on the learned geodesic distances, followed by Maximal Marginal Relevance reranking and path coherence filtering. On citation prediction benchmarks with 169K arXiv papers, GSS achieves 23\% relative improvement in Recall@20 over SPECTER+FAISS baselines. We provide a Bridge Recovery Guarantee characterizing when geodesic retrieval qualitatively outperforms direct similarity, a margin separation result connecting training loss to retrieval quality, and characterize the expressiveness of low-rank metric parameterization. Our hierarchical coarse-to-fine search with k-means pooling reduces computational cost by $4\times$ while maintaining 97\% retrieval quality.

We develop a theoretical and computational framework for beam-plasma collective oscillations in intense charged-particle beams at intermediate energies (10-100 MeV). In Part I, we formulate a kinetic field theory governed by the Vlasov-Poisson system, deriving the Lindhard dielectric function and random phase approximation (RPA) polarization tensor for three beam distribution functions. We prove via the dielectric function epsilon(omega,q)=0 the existence of undamped Langmuir wave modes above a critical beam density n_c, obtain explicit beam-plasma dispersion relations, and show that Landau damping vanishes above the particle-hole continuum. The plasma frequency Omega_p^2 = ne^2/(m*epsilon_0) is fixed by the f-sum rule independently of distribution shape; higher dispersion coefficients depend on velocity moments. Space charge effects drive anomalous beam broadening with sqrt(n-n_c) onset and Friedel oscillations at q=2k_F. The beam-plasma transition belongs to the 3D Ising universality class via renormalization group analysis. In Part II, we validate these predictions using Prometheus, a beta-VAE trained on static structure factor data S(q) from particle-in-cell (PIC) beam simulations. Prometheus detects collective plasma oscillation onset in Gaussian and uniform distributions, confirms their absence in the degenerate Fermi gas (n_c -> 0), and resolves the Kohn anomaly at q=2k_F. Dispersion analysis of S(q,omega) from PIC simulations verifies the distribution-independent Omega_p predicted by the f-sum rule. All six validation checks pass. Predicted signatures -- density-tunable plasma resonances at omega_p proportional to sqrt(n), anomalous beam broadening with sqrt(n-n_c) onset, and Friedel oscillations -- are accessible at existing intermediate-energy beam facilities.

We construct data-driven solutions to the Hubble tension, in light of recent data from the Atacama Cosmology Telescope (ACT DR6) and the Dark Energy Spectroscopic Instrument (DESI DR2). We search for the minimal modification to the recombination history through a time-varying electron mass $m_e(z)$ that increases the best-fit $H_0$ inferred from CMB data toward the SH0ES value, without worsening the fit to the data. Using Planck and ACT data including lensing, we find a perturbative modification to $m_e(z)$ that fully resolves the Hubble tension, with the solution sharing the same qualitative oscillatory structure as in previous work using Planck data alone, demonstrating its robustness to the inclusion of more precise and independent CMB data. As a byproduct, the solution also eases the $S_8$ tension. Once DESI DR2 BAO data are added, however, perturbative modifications to $m_e(z)$ cannot fully resolve the Hubble tension. This reflects the same fundamental limitation: raising $H_0$ by modifying recombination generically lowers $Ω_m$, being inconsistent with late-time cosmological observations.